Question
Find the 83rd term of the arithmetic sequence −23,−26,−29,...
Answers
GPT 3.5
To find the 83rd term of an arithmetic sequence, we can use the formula for the nth term:
aₙ = a₁ + (n-1)d
where aₙ is the nth term, a₁ is the first term, n is the number of terms, and d is the common difference.
In this case, the first term (a₁) is -23 and the common difference (d) is -3. Plugging these values into the formula, we have:
a₈₃ = -23 + (83-1)(-3)
Simplifying, we get:
a₈₃ = -23 + 82(-3)
a₈₃ = -23 - 246
a₈₃ = -269
Therefore, the 83rd term of the arithmetic sequence is -269.
aₙ = a₁ + (n-1)d
where aₙ is the nth term, a₁ is the first term, n is the number of terms, and d is the common difference.
In this case, the first term (a₁) is -23 and the common difference (d) is -3. Plugging these values into the formula, we have:
a₈₃ = -23 + (83-1)(-3)
Simplifying, we get:
a₈₃ = -23 + 82(-3)
a₈₃ = -23 - 246
a₈₃ = -269
Therefore, the 83rd term of the arithmetic sequence is -269.